An electromagnetic wave going through vacuum is described by \( E = E_0\sin(kx - \omega t) \), \( B = B_0\sin(kx - \omega t) \) then:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( E_0k = B_0\omega \)
In vacuum the electric and magnetic fields of an electromagnetic wave are in phase and their amplitudes are related by the speed of light, \( E_0 = cB_0 \). The wave given has speed \( c = \frac{\omega}{k} \) (angular frequency divided by wave number).
\( \displaystyle \frac{E_0}{B_0} = c = \frac{\omega}{k} \)
\( E_0k = B_0\omega \)
Note: A similar question was also asked in CUET (UG) 2026 on 07-06-2026 (Slot 2), on 25-05-2026 (Slot 1) and on 20-05-2026 (Slot 2), and in CUET (UG) 2023 on 14-06-2023 (Slot 1).
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
Nature of Electromagnetic Waves – “… The speed of propagation of the wave is (ω/k). … It is also seen from Maxwell’s equations that the magnitude of the electric and the magnetic fields in an electromagnetic wave are related as
\( \displaystyle B_0 = (E_0/c) \qquad (8.10) \)”